We advise you to use different colors for your pieces
as in the figure. Many people solve this puzzle in under
ten minutes, so it can't be terrible hard. But we've got
a distinct feeling that it's much harder than it ought
to be. Is this just because the pieces have such awkwardly
wriggly shapes?

THE HIDDEN SECRETS OF SOMAIt's because the Soma puzzle pieces have to satisfy
some hidden constraints as well as the obvious ones, that
it causes most people more trouble than it should.
Let's see why.
The 3 x 3 x 3 cube has 8 vertex cells,
12 edge cells, 6 face cells and
1 central cell as in fig. 2.

Figure 2. The Vertex, Edge, Face and Central (invisible) Cells.

Now the respective pieces can occupy at most

W Y G O L R B
1, 2, 2, 1, 1, 1, 1

of the vertex cells, so just one piece, the deficient
one, must occupy just one less vertex-cell than it might.
The green piece can't be deficient without being doubly so,
and therefore:

the Green piece has
its spine along an
edge of the cube.

Now let's color the 27 cells of the cube in two alternating colors,

Flame for the 14 FaVored cells, F and V,
Emerald for the 13 ExCeeded ones, E and C.

but the Yellow, Orange, bLue and Red pieces, and we now
know also the Green piece, must occupy these numbers
in every solution, and therefore so must the White
and the Black, since an interchange of colors in either or
both of these would alter the totals.

The White piece occupies
2 FV cells, 1 EC cell.

The Black piece occupies
1 FV cell and 3 EC ones.

For the placing of a single piece within the box,
these considerations leave only the positions of Fig. 3
(below). You'll see that up to rotations of the cube,
the placement of any single piece is determined by whether
or not it is deficient and whether or not it occupies the
central cell.

The hidden secrets of Soma make it quite likely that
one of the first few pieces you put in may already be
wrong, when of course you'll spend a lot of time
assembling more pieces before such a mistake shows its
effect. This would happen for instance if you started by
putting the corner of the White piece into a corner of
the cube. But if you only put the pieces into the allowed
positions, you'll find a solution almost as soon as you start.

Fig. 3. All possible Positions for the Seven Soma Pieces.

The complete list of 240 Soma solutions was made by
hand by J.H.Conway and M.J.T.Guy one particularly rainy
afternoon in 1961.